In recent years, with the great progress of technology in mobile telecommunication, cell phones have satisfied the people's desire of wireless communication and relieved users from the fetter of traditional fixed line phone. The mobile communication not only makes us be freer, but also closes the distance from people to people.
In the third generation mobile telecommunication system, the Code Division Multiple Access (CDMA) system plays an important role; however, such spreading telecommunication techniques suffer the serious problem of Multiple Access Interference (MAI), which is described as following:
Assume there are total k users in the system, and each of them transmits a set signal of binary data, which is shown as:
            b      k        ⁡          (      t      )        =            ∑              i        =                  -          ∞                    ∞        ⁢                  b                  k          ,          i                    ⁢                        P          T                ⁡                  (                      t            -                          i              ⁢                                                          ⁢              T                                )                    wherein, bk,i ∈{±1} indicates the ith data bit of the kth user, and PT(t) indicates the rectangular pulse with amplitude being 1 and period being T.
And each user respectively owns a set of spreading codes, which is shown as:
            a      k        ⁡          (      t      )        =            ∑              j        =                  -          ∞                    ∞        ⁢                  a                  k          ,          j                    ⁢                        P                      T            c                          ⁡                  (                      t            -                          j              ⁢                                                          ⁢                              T                c                                              )                    wherein, ak,j ∈{±1} indicates the jth chip of the kth user, and PTc(t) indicates the rectangular pulse with amplitude being 1 and period being Tc. Here we can define the ratio of the bit time period T to the chip time period Tc as the process gain N, that is, N=T/Tc, which is also called Spreading Factor (SF).
Therefore, the Binary Phase Shift Keying (BPSK) signals transmitted by the kth user can be shown as:sk(t)=√{square root over (2Pk)}ak(t)bk(t)wherein, Pk means the signal energy of the kth user. After transmitted through the Multi-path Fading, the signals will be received by the Rake Receiver, and the received signals is shown as:
                              r          ⁡                      (            t            )                          =                ⁢                                            ∑                              k                =                1                            K                        ⁢                                          α                k                            ⁢                                                s                  k                                ⁡                                  (                                      t                    -                                          τ                      k                                                        )                                                              +                      n            ⁡                          (              t              )                                                              =                ⁢                                            ∑                              k                =                1                            K                        ⁢                                          α                k                            ⁢                                                2                  ⁢                                      P                    k                                                              ⁢                                                          ⁢                                                a                  k                                ⁡                                  (                                      t                    -                                          τ                      k                                                        )                                            ⁢                                                          ⁢                                                b                  k                                ⁡                                  (                                      t                    -                                          τ                      k                                                        )                                                              +                      n            ⁡                          (              t              )                                                              =                ⁢                                            ∑                              k                =                1                            K                        ⁢                                          ∑                                  i                  =                                      -                    ∞                                                  ∞                            ⁢                                                ∑                                      j                    =                    0                                                        N                    -                    1                                                  ⁢                                                      α                    k                                    ⁢                                                            2                      ⁢                                              P                        k                                                                              ⁢                                      b                                          k                      ,                      i                                                        ⁢                                                                          ⁢                                      a                                          k                      ,                      j                                                        ⁢                                                                          ⁢                                                            P                                              T                        c                                                              ⁡                                          (                                              t                        -                                                  i                          ⁢                                                                                                          ⁢                          T                                                -                                                  j                          ⁢                                                                                                          ⁢                                                      T                            c                                                                          -                                                  τ                          k                                                                    )                                                                                                    +                      n            ⁡                          (              t              )                                          wherein, τk means the delay time of the kth user, ak means the Multi-path Fading, and n(t) means the Added White-Gaussian-Noise (AWGN).
The most common method for eliminating the interference caused by other users in the present day is to adopt the Interference Cancellation, which can be divided into two systems: the Successive Interference Cancellation (SIC) and the Parallel Interference Cancellation (PIC). Aimed at the PIC, the following will give a concise description.
Please refer to FIG. 1, which shows the structure diagram of the traditional Parallel Interference Cancellation with k users. Here we firstly consider the asynchronous CDMA system, in which the delay times from different users to the receiver will be different and can be arranged in order from shortest to longest as: τ1<τ2<τ3< . . . <τk. The spirit of the PIC is to eliminate all the interference caused by other users simultaneously. “STAGE 0” shown in FIG. 1 means the traditional receiver, “STAGE 1” means the first stage of the PIC, and so on, and then “STAGE s” means the sth stage of the PIC. When the receiver is in STAGE 0, for the kth user, the received signals and the kth user's spreading codes will be carried out the “Despread” operating, and thus get a value called “Decision Statisitc”, labeled as Zk,i(0); wherein, the superscript (0) means “STAGE 0”, the suffix k means “the kth user”, and the suffix i means “the ith data bit”. The formula of Zk,i(0) can be shown as:
      Z          i      ,      i              (      0      )        =            1      T        ⁢                  ∫                              i            ⁢                                                  ⁢            T                    +                      τ            k                                                              (                              i                +                1                            )                        ⁢            T                    +                      τ            k                              ⁢                        r          ⁡                      (            t            )                          ⁢                                  ⁢                              a            k                    ⁡                      (                          t              -                              i                ⁢                                                                  ⁢                T                            -                              τ                k                                      )                          ⁢                                  ⁢                  ⅆ          t                    
In STAGE 1 of the PIC, the first step is to rebuild the estimation signals, that is, to carry out the “Respread” operating with the pre-stage Decision Statisitc Zk,i(0) as well as the kth user's spreading codes so as to get an estimation value of the ith data bit in STAGE 1, which is expressed as:
            s      k              ^                  (          1          )                      ⁡          (              t        -                  τ          k                    )        =            ∑              i        =                  -          ∞                    ∞        ⁢                  2        T            ⁢              Z                  k          ,          i                          (          0          )                    ⁢                        a          k                ⁡                  (                      t            -                          i              ⁢                                                          ⁢              T                        -                          τ              k                                )                    wherein, the superscript (1) of sk^(1)(t−τk) means “STAGE 1”. Similarly, we can get other users' estimation signal values.
For the kth user, any other users are all regarded as interference. Therefore, to obtain an effect of approximated singular user, we can eliminate other users' estimation signals from the received signal. Wherein the effect of approximated singular user means the effect without MAI, which can be expressed as:
            r      k              (        1        )              ⁡          (      t      )        =            r      ⁡              (        t        )              -                  ∑                                            l              =              1                        ,                                l            ≠            k                          K            ⁢                        s          l                      ^                          (              1              )                                      ⁡                  (                      t            -                          τ              l                                )                    moreover, the Decision Statistic of STAGE 1 is expressed as:
      Z          k      ,      i              (      1      )        =            1      T        ⁢                  ∫                  T          +                      τ            k                                                              (                              i                +                1                            )                        ⁢            T                    +                      τ            s                              ⁢                                    r            k                          (              1              )                                ⁡                      (            t            )                          ⁢                              a            k                    ⁡                      (                          t              -                              i                ⁢                                                                  ⁢                T                            -                              τ                k                                      )                          ⁢                                  ⁢                  ⅆ          t                    so the formulas of the PIC in STAGE s can be shown as:    (1) The estimation signal value:
            s      k              ^                  (          s          )                      ⁡          (              t        -                  τ          k                    )        =            ∑              i        =                  -          ∞                    ∞        ⁢                  2        T            ⁢              Z                  k          ,          i                          (                      s            -            1                    )                    ⁢                        a          k                ⁡                  (                      t            -                          i              ⁢                                                          ⁢              T                        -                          τ              k                                )                        (2) The signal after removing all the interference:
            r      k              (        s        )              ⁡          (      t      )        =            r      ⁡              (        t        )              -                  ∑                                            l              =              1                        ,                                l            ≠            k                          K            ⁢                        s          l                      ^                          (              s              )                                      ⁡                  (                      t            -                          τ              l                                )                        (3) The Decision Statistic of STAGE s:
      Z          k      ,      i              (      s      )        =            1      T        ⁢                  ∫                  T          +                      τ            k                                                              (                              i                +                1                            )                        ⁢            T                    +                      τ            s                              ⁢                                    r            k                          (              s              )                                ⁡                      (            t            )                          ⁢                              a            k                    ⁡                      (                          t              -                              i                ⁢                                                                  ⁢                T                            -                              τ                k                                      )                          ⁢                                  ⁢                  ⅆ          t                    
The spirit of the PIC is to eliminate other users' estimation signals from the received signal so as to get the effect of approximated singular user. However, if there is something wrong in rk(s)(t) the signal after the interference eliminated, the Decision Statistic of STAGE s Zk,i(s) thereby may be error and furthermore the Decision Statistic of the next stage will be affected so as to result in the phenomenon of Error Propagation. Therefore, in practice, the method of Partial Interference Cancellation can be used to improve the performance of traditional PIC, and the formula can be expressed as:
            r      k              (        s        )              ⁡          (      t      )        =            r      ⁡              (        t        )              -                  P        s            ⁢                        ∑                                                    l                =                1                            ,                                      l              ≠              k                                K                ⁢                              s            l                          ^                              (                s                )                                              ⁡                      (                          t              -                              τ                l                                      )                              wherein, Ps means the Partial Factor of STAGE s, and 0<Ps<1. Such method is so-called Parallel Partial Interference Cancellation (PPIC).
However, the aforesaid PPIC needs large calculations of Respread-Despread so that it requires a very large amount of computations. In addition, the multiple-path signals are varying, which is especially a leaden encumbrance for both mobile stations and base stations. So we need a novel method to improve such problems.